You are correct and thanks for the correction, wow do I feel dumb for missing that. Maybe I can save a small scrap of face in that at least occasionally this pr

You are correct and thanks for the correction, wow do I feel dumb for missing that. Maybe I can save a small scrap of face in that at least occasionally this problem contains no such clause, e.g. the xkcd version although I should read that one again before submitting this reply.